The present invention relates to a voltage-controlled oscillator using an emitter-coupled astable multivibrator.
The voltage-controlled oscillator is frequently used in electronic devices requiring voltage to frequency conversion, such as FM modulators, PLL circuits, and voltage/frequency converters.
A conventional voltage-controlled oscillator using an emitter-coupled astable multivibrator will be described referring to FIG. 1, in terms of problems of the prior art.
In FIG. 1, transistors Q1 to Q7, resistors R1 and R2, a voltage source V1, current sources I1 and I2, and a capacitor C cooperate to form an emitter-coupled astable multivibrator. Transistors Q8 and Q9, and resistors R3 and R4 form a circuit for converting a control voltage V.sub.I of the voltage source V2 into a current. This circuit provides the operating current for the multivibrator.
FIG. 2 shows a set of waveforms of the signals at points A to D of the FIG. 1 circuit when it is operating. In the waveform diagram, the on state of the transistors Q1, Q3, Q6 and Q7 is illustrated at a high level, while the off state is shown at a low level. During a period T1, the transistors Q3 and Q7 are turned on, while the transistors Q1 and Q6 are turned off by a positive feedback circuit function. The current path of the capacitor C is routed through a path of the emitter of transistor Q7.fwdarw.capacitor C.fwdarw.collector of transistor Q8. The current determined by the collector current of the transistor Q8 flows into the capacitor C. Under this condition, the transistor Q7 is on, and therefore the emitter potential thereof is fixed. Therefore, as the capacitor C charges, the emitter potential of the transistor Q6 decreases, and then the transistor Q6 is turned on. Immediately after the transistor Q6 is turned on, the transistor Q1 is also turned on, and the transistor Q3, and Q7 are turned off by the positive feedback function. This operating state of the circuit is illustrated during a period T2 in FIG. 2. The periods T1 and T2 are alternately repeated, so that the oscillation is continued.
Let us examine the ideal oscillating frequency F.sub.I of the circuit under discussion. The base potentials V.sub.B6(2) and V.sub.B7(2) of the transistors Q6 and Q7 during the period T2 are given as: EQU V.sub.B6(2) =V.sub.CC -V.sub.BE2 -V.sub.BE5 ( 1) EQU V.sub.B7(2) =V.sub.CC -V.sub.ref -V.sub.BE1 -V.sub.BE4 ( 2)
where
V.sub.CC : Voltage of power source +B PA1 V.sub.ref : Voltage of voltage source V1 PA1 V.sub.BEn : forward voltage drop across the base and the emitter of the transistor Qn (n=1 to 9) (this is true for the equations as given below)
At this time, the transistor Q6 is turned on, and from the equation (1), we have the emitter potential V.sub.B6(2) of the transistor Q6 given by: EQU V.sub.E6(2) =V.sub.CC -V.sub.BE2 -V.sub.BE5 -V.sub.BE6 ( 3)
As seen from equation (3), the emitter potential V.sub.E7(2) of the transistor Q6 is fixed. On the other hand, since the transistor Q7 is off, the emitter potential V.sub.E7(2)E of the transistor Q7 decreases with the charging of the capacitor C. When the emitter potential E.sub.E7(2) of the transistor Q7 at the end of the period T2 drops by the forward voltage drop across the base and the emitter below the base potential V.sub.B7(2) of the transistor Q7 as given by equation (2), that is to say, as the following equation holds: EQU V.sub.E7(2)E =V.sub.CC -V.sub.ref -V.sub.BE1 -V.sub.BE4 -V.sub.BE7 ( 4)
the circuit state is inverted and returns to the period T1 state. At this time, the emitter potential V.sub.E7(1) of the transistor Q7 instantaneously changes to: EQU V.sub.E7(1) =V.sub.CC -V.sub.BE2 -V.sub.BE4 -V.sub.BE7 ( 5)
because the transistor Q7 is switched from off to on. Thus, the emitter potential of the transistor Q7 instantaneously changes from V.sub.E7(2)E to V.sub.E7(1). A potential difference between the emitter potentials V.sub.E7(2)E and V.sub.E7(1) is expressed by subtracting equation (4) from (5), we have: EQU V.sub.E7(1) -V.sub.E7(2)E =V.sub.ref ( 6)
It should be noted that the present discussion is based on the assumption that the forward voltage drops V.sub.BEn across the base and the emitter of all of the transistors are equal to one another. The potential V.sub.ref is transmitted, intact to the emitter of the transistor Q6 coupled with one end of the capacitor C. The emitter potential V.sub.E6(1)S of the transistor Q6 at the initial stage of the period T1 is: EQU V.sub.E6(1)S =V.sub.CC -V.sub.BE2 -V.sub.EB5 -V.sub.BE6 +V.sub.ref ( 7)
The above equation is led from equation (3). From this state, charging the capacitor C starts in the direction opposite that in the case of period T2. Then, the emitter potential of the transitor Q6 gradually drops and reaches the following potential: EQU V.sub.E6(1)E =V.sub.CC -V.sub.ref -V.sub.BE3 -V.sub.EB5 -V.sub.BE6 ( 8)
At this time, the circuit state instantaneously changes from the period T1 state to the period T2 state.
During the period T1, The transistor Q7 is on and its emitter potential V.sub.E7(1) is fixed as given below: EQU V.sub.E7(1) =V.sub.CC -V.sub.BE2 -V.sub.BE4 -V.sub.BE7 ( 9)
A change in the potential .DELTA.V.sub.C across the capacitor C during one period is obtained by subtracting equation (8) from equation (7) and is: EQU .DELTA.V.sub.C =V.sub.E6(1)S -V.sub.E6(1)E =2V.sub.ref ( 10)
In this case, it is assumed that the forward voltage drops V.sub.BEn across the base and the emitter of all of the transistors are equal to each other.
During period T1, the current flowing into the capacitor C depends on the collector current of the transistors Q8. During period T2, it depends on the collector current of the transistor Q9. If the transistors Q8 and Q9 have the same characteristics, and the resistors R3 and R4 have equal resistances, the collector currents of the transistors Q8 and Q9 are equal to each other. The value of this current i.sub.C is controlled by the control voltage V.sub.I, as seen from FIG. 1. The duration t of the periods T1 and T2 is: ##EQU1## where C.sub.a : Capacitance of the capacitor C.
An ideal oscillating frequency F.sub.i with a period 2t is: ##EQU2## Equation (12) teaches that the oscillating frequency F.sub.i can be linearly changed through control of the current i.sub.C by the control voltage V.sub.I.
In an actual circuit, an operation delay is inevitable due to the parasitic capacitance associated with the circuit elements, and the stray capacitance associated with the circuit wiring. This delay occurs when inverting the operation mode of the circuit, i.e. at the boundary between the periods T1 and T2. As seen from FIG. 3, there are observed delays .tau..sub.d1 and .tau..sub.d2 at the rise and fall times of the waveforms A to D and the potential difference .DELTA.V.sub.C. Using these delays .tau..sub.d1 and .tau..sub.d2, the actual oscillating frequency F.sub.r is: ##EQU3## As seen from equation (13), the actual frequency F.sub.r can also be controlled by the current i.sub.C, but the linearity of the frequency F.sub.r against the current i.sub.C deteriorates because of the presence of the term (.tau..sub.d1 +.tau..sub.d2). Since the term (.tau..sub.d1 +.tau..sub.d2) is fixed, the linearity deterioration is more marked as the frequency F.sub.r is controlled to be large (duration t is made small). The relationship between the oscillating frequency vs. the controlled voltage V.sub.I in the circuit is as shown in FIG. 4. The graph shows that nonlinearity becomes more distinctive as the oscillating frequency increases.